Method 3 -Find the circumference
from the central angle

Eratosthenes may have imagined
that the cross-section of the earth was like an grapefruit sliced in half.
You could see the sections of the orange. Also, if you walked along the
edge of the orange your path would be circular.

If you could determine the
angle that the section makes at the center and length of the edge, you
could figure out the circumference.

Here's an example. Angle
ABC is 60 degrees. Since there are 360 degrees in a circle, then there
are 6 slices in this "pie". That means that 6 arcs (AC) would fit around
the globe and if you knew that distance you would be in business!

At first glance finding
this angle seems just as impossibleas finding the diameter; but,
as it turns out, this was Eratosthenes' brilliant insight. He discovered
it by studying shadows!

Carl Sagan tells the story
of Eratosthenes in his book Cosmos (read the
excerpt.)